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SUEC 高中 Adv Maths (Irrational Part 1)
- 1. 𝒑𝒈 𝟏𝟒𝟐 𝒐𝒅𝒅 𝒆𝒗𝒆𝒏 𝟏. (𝒂) 𝟑 𝒂𝟐 − 𝟏 𝟑 = 𝒂𝟐 − 𝟏 (𝐛) 𝟔 𝒃𝟐 + 𝟏 𝟏𝟐 = 𝟔 𝒃𝟐 + 𝟏 𝟔 𝟐 = 𝒃𝟐 + 𝟏 𝟐 = 𝒃𝟒 + 𝟏 + 𝟐𝒃𝟐 𝒄 𝟓 𝒙 − 𝟐 𝟓 = 𝒙 − 𝟐
- 2. 𝒑𝒈 𝟏𝟒𝟑 𝒐𝒅𝒅 𝒆𝒗𝒆𝒏 𝒙 ≥ 𝟎 𝒙 ≤ 𝟎 𝒙 为一切实数 𝒙 为一切实数 𝒙 ≤ 𝟏 𝒙 ≥ 𝟏
- 3. 𝒑𝒈 𝟏𝟒𝟑 𝒐𝒅𝒅 𝒆𝒗𝒆𝒏 𝒙 − 𝟏 𝒙 + 𝟐 𝒂𝟒 + 𝟔𝒂𝟐 + 𝟗 𝟔𝟒𝒃𝟐 𝟐𝒙 𝟒𝒙𝟐 − 𝟐𝒂 𝟏 − 𝒙 𝟐 𝟏
- 4. 𝒑𝒈 𝟏𝟒𝟒 𝒏𝒑 𝒂𝒎𝒑 = 𝒏 𝒂𝒎 𝒑 𝒂𝒎𝒑 = 𝒂𝒎 (𝒂 ≥ 𝟎) (𝒂 ≥ 𝟎)
- 5. 𝒑𝒈 𝟏𝟒𝟓 𝒏𝒑 𝒂𝒎𝒑 = 𝒏 𝒂𝒎 𝒑 𝒂𝒎𝒑 = 𝒂𝒎 (𝒂 ≥ 𝟎) (𝒂 ≥ 𝟎) 𝒙 𝒚𝟑 𝟔 𝒙𝟐𝒚𝟑 𝟑 𝟐𝟓𝒂𝟐𝒃 𝟐𝒙𝟐 𝒚𝟑 𝟒 𝒂𝒎𝒃𝟐𝒏 𝟒 𝒙 + 𝟏 𝟑 𝒙 − 𝟏 𝟑 𝟑 𝒎𝟐 + 𝒎𝒏
- 6. 𝒑𝒈 𝟏𝟒𝟒 𝒏𝒑 𝒂𝒎𝒑 = 𝒏 𝒂𝒎 𝒑 𝒂𝒎𝒑 = 𝒂𝒎 (𝒂 ≥ 𝟎) (𝒂 ≥ 𝟎)
- 7. 𝒑𝒈 𝟏𝟒𝟓 𝒏𝒑 𝒂𝒎𝒑 = 𝒏 𝒂𝒎 𝒑 𝒂𝒎𝒑 = 𝒂𝒎 (𝒂 ≥ 𝟎) (𝒂 ≥ 𝟎) 𝟒 𝟐𝟓 𝟏𝟎 𝟑𝟐𝒎𝟓𝒏𝟓 𝟑𝟔 𝟖𝒂𝟏𝟓 𝟏𝟐 𝒙 + 𝒚 𝟔 𝟏𝟓 𝟔𝟓𝒚𝟏𝟎 𝟏𝟓 𝒚𝟑 𝟏𝟎 𝟑𝟔𝒎𝟒𝒏𝟐 𝟏𝟐 𝒙𝟐 + 𝒚𝟐 𝟔 𝟏𝟐 𝒙 + 𝒚 𝟏𝟎 ± 𝟑𝟔 𝟖𝟏𝒃𝟒 − 𝟏𝟖 𝒙𝟏𝟐 𝟏𝟖 𝟔𝟒𝒙𝟑𝒚𝟑 𝟏𝟖 𝟔𝟒𝒙𝟖𝒚𝟏𝟎
- 8. 𝒑𝒈 𝟏𝟒𝟓 𝒏𝒑 𝒂𝒎𝒑 = 𝒏 𝒂𝒎 𝒑 𝒂𝒎𝒑 = 𝒂𝒎 (𝒂 ≥ 𝟎) (𝒂 ≥ 𝟎) 𝟖. 𝟗𝟒 𝟐. 𝟐𝟒 𝟓. 𝟐𝟎 𝟏. 𝟕𝟑 𝟐. 𝟖𝟑 𝟏. 𝟒𝟏
- 9. 𝒑𝒈 𝟏𝟒𝟔 𝒏 𝒂𝒃 = 𝒏 𝒂 𝒏 𝒃 𝒏 𝒂 𝒃 = 𝒏 𝒂 𝒏 𝒃 𝒂 ≥ 𝟎 (𝒃 ≥ 𝟎) (𝒂 ≥ 𝟎) (𝒃 ≥ 𝟎) 𝒏 𝒂 𝒎 = 𝒏 𝒂𝒎 (𝒂 ≥ 𝟎) 𝒎 𝒏 𝒂 = 𝒎𝒏 𝒂 (𝒂 ≥ 𝟎)
- 10. 𝒑𝒈 𝟏𝟒𝟔
- 11. 𝒑𝒈 𝟏𝟒𝟔 𝟏𝟒𝟎𝟖 − 𝟓𝟎𝟒 𝒂𝒃𝟐 𝒂𝟑 𝒃𝒕𝟒 𝟐𝒂𝟐 𝒃𝟑 𝒂𝟐 𝒃𝒄𝟑 𝟐 𝟗 𝟑 𝟐 𝟑 𝒏 𝟕𝒎𝟐 𝟒 𝒂𝟑 𝟐𝒃 𝟐𝒙𝒚𝟐 𝟑𝒂𝟐𝒃𝟑 𝒂𝒃𝟐 𝒄𝟑𝒅 𝟑 𝒂𝟐𝒃𝟐 𝟗 𝟓 𝒂𝟐𝒃𝟒 𝒎𝟑 𝟒 𝟏𝟐𝟓𝒏𝟑
- 12. 𝒑𝒈 𝟏𝟒𝟕 − 𝒙𝟑 𝒚𝟑 𝟒 𝒚𝟑 𝒙𝟑 𝟔 𝒂𝒃 𝟔 𝟐𝟖 𝟑 𝒂 𝟐 𝟑 𝒂𝟐
- 13. 𝒑𝒈 𝟏𝟒𝟕 − 𝟏𝟒𝟗 𝟐𝒂 𝟐𝒂 𝟒𝒕𝟐 𝒕 𝟒𝒑𝒒𝟑 𝒑𝒒 𝒕 𝟑 𝟐𝒕 𝟑𝒂 𝟑 𝒂𝟐 𝟐𝒂𝒃 𝟐𝒂𝒃𝟐
- 14. 𝒑𝒈 𝟏𝟒𝟕 − 𝟏𝟒𝟗 𝟕𝟓 𝟏𝟔 𝒃𝟑𝒄 𝒙𝟒 𝒚 𝟑 𝟕𝟐 𝟑 𝒙𝟏𝟎 𝒚 𝒏 𝟒𝒏 𝒂𝒏−𝟏
- 15. 𝒑𝒈 𝟏𝟒𝟖
- 17. 𝒑𝒈 𝟏𝟒𝟖
- 18. 𝒑𝒈 𝟏𝟒𝟗 𝟒𝒄 𝟑𝒂𝟑𝒃 𝒂𝒃𝒄 𝒙 𝟑𝒎𝒏 𝟑 𝒂𝒎 𝟒 𝒏𝟐 + 𝟏 𝟏 𝒙 𝟑 𝟐𝒙𝒚 𝒃 𝟔𝒂𝟑 𝟑 𝟒𝒂𝟐𝒃 𝒙𝒚𝟐 𝟐 𝟑 𝟏𝟐𝒙𝒚𝟐 𝒂 𝟑 𝒂𝒃𝟐 𝟗𝒂𝒃 𝟓 𝒂𝟑𝒃 𝒎𝟑𝒏 𝟒 𝒎𝟑𝒏𝟐 − 𝒙 𝒚𝟐 𝒙𝒚 𝟔 𝟐𝟖 𝟔 𝒂𝟐
- 19. 𝒑𝒈 𝟏𝟒𝟗 = − 𝒙 𝒚𝟐 𝒙𝒚 𝟐𝟖. − 𝒙 𝒚 𝒚 𝒙 𝟑 = − 𝒙𝟑 𝒚𝟑 𝒚𝟐𝒚 𝒙𝟐𝒙 = − 𝒙𝟑 𝒚 𝒙𝒚𝟑 𝒚 𝒙 = − 𝒙𝟐 𝒚𝟐 𝒚 𝒙 × 𝒙 𝒙 𝟏𝟖. 𝒏 𝟑 𝒚𝟐𝒏+𝟏 = 𝒏 𝟑 𝒏 𝒚𝟐𝒏 × 𝒚 = 𝟏 𝒚𝟐 × 𝒏 𝟑 𝒏 𝒚 × 𝒏 𝒚𝒏−𝟏 𝒏 𝒚𝒏−𝟏 = 𝟏 𝒚𝟑 𝒏 𝟑𝒚𝒏−𝟏
Notas del editor
- https://www.onlinemathlearning.com/indices-negative-fractional.html
- Let x represent a real number, find the conditions under which the following formulas have meaning. x be all real numbers
- simplify the exponents and root exponents of the roots in the following radical formula
- 8. Hint = take out m square
- Change to same root